2015/11/20 by Hatem Hajlaoui, hajlaoui, Hatem, Abdellaziz Harrabi +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1511.06736
openalex publication_date 2015/11/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We examine the general weighted Lane-Emden system n -
Delta u =
rho(x)vp,
quad -
Delta v=
rho(x)u^
theta,
quad u,vgt;0
quad\n
mboxin
;
mathbbRN n where 1<p\≤\θ and\n \ρ: \ℝN\→ \ℝ is a radial continuous function\nsatisfying\n \ρ(x)\≥ A(1+|x|2)\(\α)/(2) in \ℝN for some\n\α\≥ 0 and A>0. We\n prove some Liouville type results for stable solution and improve the\nprevious works citeco, Fa, HU. In particular, we establish a new comparison\nproperty\n (see Proposition 1.1 below) which is crucial to handle the case 1 < p \≤\n\(4)/(3). Our results can be applied also to the weighted Lane-Emden\nequation -\Δ u = \ρ(x)up in \ℝN.\n